The unknown Muguruza required less than an hour and a half to defeat the other half of golfing world number one Rory McIlroy 6-2 6-4.
Expectations were high coming into Miami for the former world number one after she enjoyed a run to the final in Indian Wells just last week, before being beaten by world number two Maria Sharapova in the championship match.
But Muguruza becomes the latest in a line of unexpected defeats for the Dane, after she also lost to China’s Wang Qiang at the Malaysian Open and unseeded Svetlana Kuznetsova at the Australian Open.
Li Na is the next mountain for Muguruza to climb after the Chinese fifth seed saw off Varvara Lepchenko 6-2 6-4.
Top ranked Serena Williams overcame a slow start to turn away Japan's Ayumi Morita 6-3 6-3 in third round play, but Venus was forced to withdraw from the tournament with a back injury.
Serena Williams, seeking a record sixth Miami title, fell 3-0 behind in the first set against her Japanese opponent but capitalised on four of her six break points to win.
The loss left Morita 0-19 against top 10 players, while Serena reamined on course to break a tie with Steffi Graf for the most singles titles in the tournament.
Venus Williams, however, pulled out of the tournament with a lower back injury before her match with fellow American Sloane Stephens.
"This is just the kind of tournament you want to play well at," Venus said. "But I have faced disappointments in my life and my career. It's not the first and probably not the last."
World number four Agnieszka Radwanska was pushed hard by Slovakia's Magdalena Rybarikova before eventually coming through 7-6(5) 2-6 6-3 while Venus Williams was forced to retire with a back injury without even hitting a ball against compatriot Sloane Stephens.
WTA Sony Open round three results
1-Serena Williams (U.S.) beat Ayumi Morita (Japan) 6-3 6-3
13-Dominika Cibulkova (Slovakia) beat Romina Oprandi (Switzerland) 6-3 6-4
4-Agnieszka Radwanska (Poland) beat Magdalena Rybarikova (Slovakia) 7-6(5) 2-6 6-3
Garbine Muguruza Blanco (Spain) beat 9-Caroline Wozniacki (Denmark) 6-2 6-4
Ajla Tomljanovic (Croatia) beat Andrea Petkovic (Germany) 0-6 6-4 7-6(1)
5-Li Na (China) beat 25-Varvara Lepchenko (US) 6-2 6-4
16-Sloane Stephens (U.S.) beat 19-Venus Williams (US)WO
30-Kirsten Flipkens (Belgium) beat 7-Petra Kvitova (Czech Republic) 6-0 4-6 6-1